You do need the extra rest and a 90-minute or longer nap would be a good idea under those circumstances IMO. As a point of reference to the amount of sleep required, let me quote something from the January/February 2001 issue of Muscle Media.
Get Nine Hours of Sleep Per Night. Nine hours of sleep may sound like a lot, especially to those of us who are used to "getting by" with no more than seven. However, in a study published this past March in the Tufts University Health & Nutrition Letter, researchers from the school's department of nutrition science discovered that people who slept an average of seven hours a night had significantly higher levels of cortisol in the afternoon than when they slept for nine hours a night. And as we've already seen, elevated cortisol levels may lead to unwanted bodyfat accumulation around the belly. So, to help keep cortisol levels in check, try to get at least nine hours of sleep per night.